The equation of a circle $C$ is $x^2+y^2+18y+32 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2) + (y^2+18y) = -32$ $(x^2) + (y^2+18y+81) = -32 + 0 + 81$ $x^2 + (y+9)^{2} = 49 = 7^2$ Thus, $(h, k) = (0, -9)$ and $r = 7$.